Well, I've never expected him to be some great manager but I think finishing 5th with spurs in his first season will be a pretty decent finish. It only looks worse because of the good start they made and the way they've lost some games.
It's not a bad start to his spurs career and certainly deserves a crack next season to see if he can improve on it. Arsenal may not be challenging for titles now if they got rid of Arteta when he was finishing 5th just a couple of years ago.
Football is a funny game. If you asked us 2 years ago, I wouldn't have picked Arteta's Arsenal to be our next big rival, half the Arsenal fans wanted him gone, but you give a manager a bit of time to get things together and things can change.
I think Spurs should stick with him and give him a bit of time, see how it goes. Finishing around 5th with spurs is hardly some awful season.